Optical proximity correction or OPC is a technique that has been used in semiconductor device fabrication to produce sub-micron integrated circuit feature sizes. OPC applies systematic changes to photomask geometries to compensate for non-linear distortions caused by optical diffraction, as well as photoresist development and etch process effects.
OPC model regression may use the definitive search method and the conjugate gradient method. The definitive search method calculates all the grid points of parameter space to obtain the best parameters to minimize or maximize a merit function. The merit function depends on the deviations between model-predicted values and experimental data. The conjugated gradient method optimizes the merit function to obtain the best parameters by means of the gradients of the current parameters. However, vast computation power and resources are needed to compute the dense grid points and inaccurate results for sparse calculation grids make the definitive search method impractical. The conjugate gradient method is inefficient because of the large estimation errors of the gradients for non-linear systems and local optimization characteristics.